Electromagnetism Summary

Magnetic Fields and Forces

Magnetic Field from Current in Wire

The direction of the magnetic field around a wire carrying current is determined by the right-hand rule. If the current flows out of the page, the magnetic field lines form circles around the wire.

Force on a Moving Charge

A positive charge moving parallel to a current-carrying wire experiences a magnetic force. The direction of the force depends on the direction of the current and the charge's velocity.

Force on Current-Carrying Wire in Magnetic Field

A wire carrying current in a magnetic field experiences a force. The direction of the force is determined by the right-hand rule.

Equilibrium of Wire in Magnetic Field

A wire can be held in equilibrium in a magnetic field if the magnetic force balances the gravitational force. The length of the wire needed for equilibrium can be calculated using F = I L B.

Alpha Particle in Electric and Magnetic Fields

An alpha particle accelerated through a potential difference gains speed, calculated by PE = qV. Entering a magnetic field, it experiences a magnetic force F = qvB, causing it to move in a circular path with radius r = \frac{mv}{qB}.

Magnetic Field due to a Wire Segment

The magnetic field at points near a wire segment can be calculated using the Biot-Savart law.

Magnetic Force Between Parallel Wires

Parallel wires carrying current exert a magnetic force on each other. The force per unit length is given by F = I L B. Wires with currents in the same direction attract, while wires with currents in opposite directions repel.

Faraday's Law and Lenz's Law

Changing magnetic flux through a loop induces a current. The direction of the induced current opposes the change in flux based on Lenz's Law.

Force on a Proton in a Magnetic Field

A proton moving in a magnetic field experiences a force F = qvB. The acceleration of the proton is a = \frac{F}{m}.

Proton in Circular Motion

A proton moving perpendicular to a magnetic field travels in a circle path. The radius is given by r = \frac{mv}{qB} and angular velocity w = \frac{v}{r}.

Force on a Wire in Magnetic Field

The force on a wire in a magnetic field is F=ILB.

Right-Hand Rule

The right-hand rule is used to determine the direction of force, magnetic field, or velocity.